Athermal integrated optical waveguide device

ABSTRACT

An athermalized integrated optical waveguide device in which thermal spectral shifts are inhibited is provided and in which the light transmitting properties are insensitive to temperature variations and fluctuations. The athermalized integrated optical waveguide device has at least two waveguide core arms, preferably comprised of a silica glass, with the core arms cladded with a waveguide cladding composition, preferably a silica glass that has a boron concentration different than the cores. The first waveguide arm and the second waveguide arm have a difference in an effective index thermal slope in order to provide an athermalized device such as an intereferometer on a substantially planar substrate. In addition the at least two waveguide core arms are comprised of path segments having different waveguide core dimensions.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention relates to an integrated optical waveguide device in which thermal spectral shifts are inhibited, and particularly to athermalized optical waveguide devices in which the light transmitting properties are insensitive to temperature variations and fluctuations.

[0003] 2. Technical Background

[0004] Integrated optical waveguide devices, such as integrated optical circuits, combine miniaturized waveguides and optical devices into a functional optical system incorporated onto a small planar substrate. Such integrated optical waveguide devices are utilized in optical communications systems, usually by attaching optical waveguide fibers, that transmit light signals to the integrated optical waveguide device as inputs and outputs. The integrated optical waveguide device performs a function or process on the transmitted light in the optical communications system. Such devices provide good performance at consistent standard room temperatures but exhibit thermal spectral shifts (dλ/dT, measured in nm/° C.) and related poor performance when used in environments where they are exposed to thermal variations and fluctuations in temperature.

[0005] Integrated optical devices which incorporate interferometers, particularly interferometers based on the division of amplitude, such as Mach-Zehnder interferometers which depend on amplitude splitting of a wavefront, can be used as transmitting filters, sensors, and wavelength multiplexing and demultiplexing devices.

[0006] Integrated optical devices which incorporate an interferometer are particularly useful as a wavelength division multiplexer/demultiplexer. Such wavelength multiplexer/demultiplexers may incorporate a phased array comprised of a plurality of different waveguide core arms.

[0007] It has been found that the use of integrated optical waveguide devices is limited by their temperature dependence. In such integrated devices, thermal spectral shifts of greater than or of the order of about 0.001 to 0.01 nm/° C. at a transmitting wavelength of 1550 nm can limit their usefulness in environments of differing temperature.

SUMMARY OF THE INVENTION

[0008] Accordingly the present invention is directed to an optical waveguide device that substantially obviates one or more of the problems due to limitations and disadvantages of the related art.

[0009] Additional features and advantages of the invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the compositions, structures, design, and methods particularly pointed out in the written description and claims hereof as well as the appended drawings.

[0010] To achieve these and other advantages and in accordance with the purpose of the invention, as embodied and broadly described, the invention provides an athermalized integrated optical waveguide device having at least two waveguide core arms with the core arms cladded with a waveguide cladding composition, preferably a silica glass that has a boron concentration different than the cores. Preferably the at least two waveguide core arms are of the same core composition, preferably a silica glass.

[0011] In another aspect, the invention includes an athermal optical waveguide device having at least two waveguide core arms which are comprised of path segments having different waveguide core dimensions.

[0012] A further aspect of the invention is to provide a method of athermalizing an optical waveguide device by forming at least two waveguide core arms having path segments of unequal waveguide core widths and cladding the waveguide core arms with a cladding composition having a concentration of boron different than the waveguide core arms.

[0013] It is to be understood that both the foregoing general description, and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.

[0014] The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate several embodiments of the invention and, together with the description, serve to explain the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015]FIG. 1 comprises a schematic representation of an inventive integrated Mach-Zehnder interferometer optical waveguide device.

[0016]FIG. 2 comprises a cross-section view of the inventive integrated Mach-Zehnder interferometer optical waveguide device showing channel waveguide widths.

[0017]FIG. 3 comprises a cross-section view of the inventive integrated Mach-Zehnder interferometer optical waveguide device showing channel waveguide thickness.

[0018]FIG. 4 comprises a schematic representation of an inventive integrated optical multiplexer/demultiplexer waveguide device.

[0019]FIG. 5 comprises a schematic representation of an inventive integrated optical multiplexer/demultiplexer waveguide device.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] The athermalized integrated optical waveguide device of the invention includes a first waveguide core arm and at least a second waveguide core arm, and a waveguide cladding which clads the waveguide core arms.

[0021] The athermalized waveguide device comprises a first waveguide core arm, a second waveguide core arm, wherein the first and second waveguide core arms are comprised of a core composition, a waveguide cladding, said waveguide cladding cladding said waveguide core arms, said waveguide cladding comprised of a cladding composition, wherein said core composition and said cladding composition have a difference in thermal spectral index shift slope (nm/° C.). The difference in thermal spectral index shift slope (nm/° C.) is preferably negative but may be positive. Preferably the core composition comprises a silica glass core composition. Preferably the cladding composition comprises a silica glass cladding composition. Said silica glass core composition and said silica glass cladding composition preferably have a difference in concentration of a dopant for controlling thermal spectral index shift slope (nm/° C.), wherein said two waveguide arms have a difference in effective index thermal slope d(N₁−N₂)/dT, where N₁ and N₂ are the effective indices of the fundamental modes of the first and second waveguides, preferably wherein said difference in concentration of dopant for controlling thermal spectral index shift slope (nm/° C.) is a difference in boron concentration.

[0022] The cladding composition and the core composition have different material based physical properties such as the thermal variation of the index of refraction (dn/dT) and thermal expansion (∝=(1/L)(dL/dT)). For example adding B₂O₃ to the silica glass compositions reduces the thermal variation of the index of refraction (dn/dT). The material based physical properties differences between the cladding composition and the core composition, in conjunction with waveguide effects, such as width differences, combine to change the thermal spectral shifts of the waveguide device (dλ/dT, measured in nm/° C.).

[0023] Preferably the first waveguide core arm is comprised of a path segment having a waveguide core dimension of w₁ and said second waveguide core arm is comprised of a path segment having a waveguide core dimension of w₂ wherein w₁ is not equal to w₂, preferably said waveguide core dimension of w₁ and said waveguide core dimension of w₂ are waveguide core width, and less preferably are waveguide core thickness.

[0024] In addition, the first waveguide core arm may be comprised of a path segment having a waveguide core dimension of w₁ and a path segment having a waveguide core dimension of w₂, and said second waveguide core arm may be comprised of a path segment having a waveguide core dimension of w₁ and a path segment having a waveguide core dimension of w₂, wherein the length of said first waveguide core arm path segment having a waveguide core dimension of w₁ is not equal to the length of said second waveguide core arm path segment having a waveguide core dimension of w₁, preferably wherein the length of said first waveguide core arm path segment having a waveguide core dimension of w₂ is not equal to the length of said second waveguide core arm path segment having a waveguide core dimension of w₂.

[0025] The optical waveguide device may include a planar substrate and may comprise an interferometer, a filter, a wavelength division multiplexer/demultiplexer, or a phased array.

[0026] Reference will now be made in detail to the present preferred embodiments of the invention, an example of which is illustrated in accompanying drawing FIG. 1.

[0027] The exemplary embodiment of the inventive waveguide device of the present invention is shown in FIG. 1 and is designated generally by reference numeral 20.

[0028] In FIG. 1 athermalized integrated optical waveguide device 20 includes a first waveguide core arm 32 and a second waveguide core arm 34. First and second waveguide core arms 32 and 34 are comprised of a silica glass core composition. As shown in FIG. 2, first and second waveguide core arms 32 and 34 are cladded with a waveguide cladding 38 comprised of a silica glass cladding composition. The silica glass core composition of first and second waveguide core arms 32 and 34 and the silica glass cladding composition of waveguide cladding 38 have a difference in boron concentration. The cladding composition and the core compositions have different boron concentrations, one of which may be zero. Boron is a silica glass index depressing dopant which reduces the thermal variation of the index of refraction. Boron is a dopant which provides for controlling the thermal spectral index shift slope (nm/° C.), wherein the difference in boron concentration is a difference in concentration of dopant for controlling thermal spectral index shift slope (nm/° C.).

[0029] First waveguide core arm 32 is comprised of a path segment 42 having a waveguide core dimension of w₁. Second waveguide core arm 34 is comprised of a path segment 44 having a waveguide core dimension of w₂.

[0030] As shown in FIG. 2, in the preferred embodiment, dimensions w₁ and w₂ are waveguide core widths. The first waveguide core arm 32 of optical waveguide device 20 is comprised of a path segment 42 having a waveguide core width dimension of w₁. The second waveguide core arm 34 is comprised of a path segment 44 having a waveguide core width dimensions of w₂, wherein the widths w₁ and w₂ are not equal, and are substantially different.

[0031] As shown in FIG. 3, first waveguide core arm 32 is comprised of a path segment 42 which may have a waveguide core thickness dimension of w₁. Second waveguide core arm 34 comprised of path segment 44 may have a waveguide core thickness dimension of w₂. First waveguide core arm path segment 42 may have a waveguide core thickness and width dimensions different from second waveguide core arm path segment 44.

[0032] The silica glass core composition of the invention is preferably comprised of GeO₂, B₂O₃, P₂O₅, and SiO₂. More preferably, the silica glass core composition comprises 10-20 wt. % GeO₂, 0-2 wt. % B₂O₃, 0-2 wt. % P₂O₅, and 60-90 wt. % SiO₂. Most preferably the silica glass core composition comprises about 15 wt. % GeO₂, about 1 wt. % B₂O₃, about 1 wt. % P₂O₅, and about 83 wt. % SiO₂.

[0033] The silica glass cladding composition of the invention is preferably comprised of B₂O₃, P₂O₅, and SiO₂. More preferably the silica glass cladding composition comprises 3-13 wt. % B₂O₃, 0-5 wt. % P₂O₅, and 75-97 wt. % SiO₂. Most preferably the silica glass cladding composition comprises about 8 wt. % B₂O₃, about 2 wt. % P₂O₅, and about 90 wt. % SiO₂.

[0034] The silica glass core composition and the silica glass cladding composition preferably have a boron concentration difference in the range of about 3 wt. % B₂O₃ to about 11 wt. % B₂O₃. This boron concentration difference between the core and the cladding is more preferably in the range of about 5 wt. % B₂O₃ to about 9 wt. % B₂O₃, even more preferred in the range of about 6 wt. % B₂O₃ to about 8 wt. % B₂O₃, and most preferably about 7 wt. % B₂O₃.

[0035] Preferably, the first and second waveguide arms 32 and 34 are comprised of the same silica glass core composition with said first and second waveguide arms glass core compositions being formed concurrently from the same glass forming source, preferably as a uniform glass layer of homogeneous composition formed from a commonly mixed silica core glass feedstock which is converted preferably through oxidation into the glass.

[0036] Preferably, waveguide cladding 38 overlays first and second waveguide core arms 32 and 34 as a overclad layer of uniform composition formed from a commonly mixed silica cladding glass feedstock which is converted preferably through oxidation into the glass.

[0037] Preferably the silica glass core composition is formed by flame hydrolysis conversion of a commonly mixed silica core glass feedstock comprised of halide-free organometallic source compounds. Preferably the silica glass cladding composition is formed by the flame hydrolysis conversion of a commonly mixed silica cladding glass feedstock comprised of halide-free organometallic source compounds. Preferably the source compound for SiO₂ is octamethylcyclotetrasiloxane, for GeO₂ is germanium ethoxide, for B₂O₃ is triethylborate, and for P₂O₅ is trimethylphosphate.

[0038] Optical waveguide device 20 comprises a silica glass substrate 40, which provides a base for the formation of the device waveguides such as first and second waveguide core arms 32 and 34. Substrate 40 may comprise a silicon substrate having a buffer layer.

[0039] As shown in FIG. 1, preferably first waveguide core arm path segment 42 having the waveguide core width w₁ is substantially parallel with the second waveguide core arm path segment 44 having the waveguide core width w₂.

[0040] In the Mach-Zehnder interferometer optical waveguide device 20, the optical path length of first waveguide core arm 32 is not equal to the optical path length of second waveguide core arm 34. The physical path length of first waveguide core arm 32 is not equal to the physical path length of second waveguide core arm 34 as measured from Y coupler 30 to proximity coupler 36. In an alternative embodiment a balanced Mach-Zehnder interferometer can be utilized where both arms are of equal physical length, but have unequal optical path length. In Mach-Zehnder interferometer optical waveguide device 20, first waveguide core arm 32 is comprised of path segments 46 having a waveguide core width of w₃. First waveguide core arm 32 includes adiabatic tapers 48 between path segments 46 and path segment 42. Adiabatic tapers 48 connect the w₃ core width of path segment 46 with the w₁ core width of path segment 42. Second waveguide core arm 34 includes adiabatic tapers 50 between path segments 46 and path segment 44. Adiabatic tapers 50 connect the w₃ core width of path segment 46 with the w₂ core width of path segment 44. The length of first waveguide core arm path segment 42 having the w₁ waveguide core width is substantially equal to the length of second waveguide core arm path segment 44 having the w₂ waveguide core width.

[0041] The invention further includes an integrated optical waveguide device 20, preferably an athermalized Mach-Zehnder interferometer, comprised of at least two unequal optical path length waveguide paths 32 and 34 of the same core glass composition comprised of GeO₂, B₂O₃ P₂O₅, and SiO₂, which are cladded with a clad glass composition comprised of B₂O₃ P₂O₅, and SiO₂, having a B₂O₃ concentration different than the core glass composition, wherein the at least two unequal length paths 32 and 34 include respectively path segments 42 and 44 of different path segment widths. The difference of widths between the path segments 42 of path 32 and 44 of path 34 provide a means for varying the fraction of the mode field propagated in the waveguide paths. Preferably the path segments 42 and 44 of different widths have the same length.

[0042] The invention further includes an integrated optical waveguide interferometer comprising: a first channel waveguide arm and a second channel waveguide arm, said channel waveguide arms having a difference in length of ΔL, said channel waveguide arms comprised of a core composition, said first channel waveguide arm including a segment of length L_(w) having a channel waveguide width w₁ and a mode field effective index N₁ dependent on the channel waveguide width w₁, said first channel waveguide arm including a segment having a channel waveguide width w₃ and a mode field effective index N₃ dependent on the channel waveguide width w₃, said second channel waveguide arm including a segment of length L_(w) having a channel waveguide width w₂ and a mode field effective index N₂ dependent on the channel waveguide width w₂, said second channel waveguide arm including a segment having a channel waveguide width w₃ and a mode field effective index N₃ dependent on the channel waveguide width w₃, a waveguide cladding composition, said waveguide cladding composition cladding said channel waveguide arms, said cladding composition having a concentration of a dopant for controlling thermal spectral index shift slope (nm/° C.), wherein ΔB is the difference between the concentration of the dopant in the core composition and the cladding composition, said integrated optical waveguide interferometer being substantially insensitive to a temperature T change when ${{{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}L_{w}}} \cong O},$

[0043] preferably wherein said dopant for controlling thermal spectral index shift slope (nm/° C.), comprises boron.

[0044] The method of making the optical waveguide devices of the invention includes the method of athermalizing the optical waveguide devices to inhibit thermal spectral shifts. The inventive method of making an optical waveguide device includes the step of providing a first waveguide arm 32 and a second waveguide arm 34, with the waveguide arms having a difference in length of −L; the waveguide arms comprised of a core composition having a high index of refraction, the first waveguide arm including a segment 42 of length L_(w) having a waveguide width w₁, the remainder of said first waveguide arm having a waveguide width w₃, the second waveguide arm 34 including a segment 44 of length L_(w) having a waveguide width w₂, and the remainder of said second waveguide arm having a waveguide width w₃. The inventive method includes the step of cladding the waveguide arms with a cladding composition having a low index of refraction, said cladding composition having a boron concentration different from the boron concentration of the core composition, wherein −B is the difference between the boron concentration of the core composition and the cladding composition. The method further includes the step of athermalizing the optical waveguide device by optimizing

[0045] −L, L_(w), w₁, w₂, w₃, and −B to provide a zero or near zero thermal spectral shift when subjected to a change in temperature T. The segment 42 of length L_(w) having a waveguide width w₁ has a mode field effective index N₁ dependent on the width w₁. The segment 44 of length L_(w) having a waveguide width w₂ has a mode field effective index N₂ dependent on the width w₂. The remainder of the first and second waveguide arms 32 and 34 have a waveguide width of w₃ with a mode field effective index N₃. The method of making the optical waveguide device includes the step of athermalizing the device by providing N₃, −L, N₂, N₁, and L_(w) according to the equation: ${{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}L_{w}}} \cong O$

[0046] The invention further includes a method of making an optical waveguide device 20 preferably a Mach-Zehnder interferometer embodied in an integrated optical circuit, having the step of providing an optical waveguide device substrate 40. Preferably the optical waveguide device substrate is comprised of silica glass, most preferably fused silica. The method further includes the step of forming a first waveguide core arm 32 of a silica glass core composition of high refractive index, first waveguide core arm 32 including a path segment 42 having a waveguide core width of w₁ and a path segment 46 having a waveguide core width of w₃, first waveguide core arm 32 having a length of L₁. The method includes the step of forming a second waveguide core arm 34 of said silica glass core composition, second waveguide core arm 34 including a path segment 44 having a waveguide core width of w₂ and a path segment 46 having a waveguide core width of w₃, second waveguide core arm 34 having a length L₂ not equal to the length L₁ of first waveguide core arm 32. The method further includes the step of cladding first and second waveguide core arms 32 and 34 with a silica glass cladding composition of low refractive index. The method includes providing the silica glass core composition with a boron concentration B_(core). The method further includes the step of providing the silica glass cladding composition with a boron concentration B_(clad) different from the silica glass core composition boron concentration B_(core).

[0047] Preferably the step of forming first waveguide core arm 32 and second waveguide core arm 34 includes the step of depositing a core layer of the silica glass core composition over the silica glass substrate and the step of exposing the deposited core layer with an image containing a pattern of first waveguide core arm 32 and second waveguide core arm 34. Preferably this method utilizes photolithography techniques in which a mask containing the planar pattern of the waveguide arms and optical circuitry of optical waveguide device 20 including the appropriate size, orientation, placement, and shape of elements such as couplers 30 and 36, waveguide segments 46, 44, 42, adiabatic tapers 48 and 50, input waveguide 24, and output waveguides 26 and 28 is used with light to expose an image of the pattern on the core composition. Such light exposure effects a chemical change in the exposed areas compared to the unexposed areas. Chemical processing techniques such as etching, preferably reactive ion etching, are used to remove the exposed or unexposed areas to result in waveguide arms 32 and 34 and the other elements of optical waveguide device 20 and its optical circuitry. Exposure and removal techniques can be utilized to adjust the depth of formed waveguides and elements. Exposure and removal techniques can also be utilized to adjust the resolution, width, and other dimensions of the pattern image and the formed waveguides and elements. Such exposure, chemical processing, and removal techniques can be utilized to change and adjust the optical properties and characteristics of the waveguides, such as to change or adjust the optical path lengths of the waveguides.

[0048] Preferably the method step of forming first waveguide core arm 32 and second waveguide core arm 34 includes the step of forming first waveguide core arm path segments 42 having a waveguide core width of w₁ substantially parallel to second waveguide core arm path segment 44 having a waveguide core width of w₂. Preferably the method further includes forming first waveguide core arm path segment 42 having a waveguide core width of w₁ with a length of L_(w) and second waveguide core arm path segment 44 having a waveguide core width of w₂ with a substantially equal length of L_(w). Preferably the method includes the step of optimizing w₃, L₁, L₂, w₁, w₂, L_(w), and the difference between B_(core) and B_(clad) to provide an athermal optical waveguide device having a minimal or no dependence on temperature T, more preferably an athermal amplitude interferometer, and most preferably a Mach-Zehnder interferometer.

[0049] An athermal Mach-Zehnder interferometer optical waveguide device 20 may be produced, utilizing straight waveguide path segments 42 and 44 having the same length L_(w) and different widths, w₁ and w₂, to vary the fraction of the mode field which is propagated within the core and clad layer compositions which have different boron concentrations, resulting in minimal temperature dependence.

[0050] In athermalized optical waveguide device 20, the same silica glass core composition is used for each of the interferometer arms 32 and 34. Also, the same silica glass cladding composition is used to clad arms 32 and 34 with cladding 38. Straight waveguide path segment 42 having a waveguide core width of w₁, of first waveguide core arm 32 and straight waveguide path segment 44 having a waveguide core width of w₂ of second waveguide core arm 34, have the same length L_(w), so that the path length difference −L between first waveguide core arm 32 and second waveguide core arm 34 is not changed but their different widths w₁ and w₂ vary the fraction of the mode field which is propagated within the core and clad layers which have a boron concentration difference −B. The preferred boron concentration B_(core) of the silica glass core composition which comprises the core is 1 wt. % boron (B₂O₃). The preferred boron concentration B_(clad) of the silica glass cladding is 8 wt. % boron (B₂O₃). This provides an appropriate and preferred −B of about AB=B_(core)−B_(clad)=−7 wt. % boron (B₂O₃). Path segment 42 of waveguide core width w₁ and path segment 44 of waveguide core width w₂ are utilized in the invention without additional loss by providing adiabatic tapers 48 and 50 between the path segments of different width to couple these waveguides of different widths. Path segment 42 may have an enlarged width w₁ which may be multimode but this does not impact the response of the device because only the fundamental mode is excited and any residual light coupled to higher order modes is eliminated by waveguides 46 located after path segment 42. The length of waveguides 46 after path segments 42 and 44 may be increased as needed to obtain the filtering effect while not changing −L.

[0051] Mach-Zehnder interferometer optical waveguide device 20 when made with the athermalization condition of: ${{{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}L_{w}}} = 0};$

[0052] provides an athermalized optical waveguide device 20.

[0053] Optical waveguide device 20 functions as a Mach-Zehnder interferometer when the Optical Path Difference (OPD) and constructive interference conditions are met according to the following equation:

OPD=(N ₃)(ΔL)+(N ₂ −N ₁)(L _(w))=mλ;

[0054] wherein N₃ is the mode effective index associated to the waveguide width w₃ of waveguide arm path segments 46, N₁ is the mode effective index associated to the waveguide width w₁ of first waveguide arm path segment 42, N₂ is the mode effective index associated to the waveguide width w₂ of second waveguide path segment 44, −L is the path length difference between first waveguide core arm 32 and second waveguide core arm 34 L_(w) is the length of path segments 42, 44, m is an integer number, and Σ is the wavelength of light transmitted through optical waveguide device 20.

[0055] The thermal spectral shift of the optical waveguide device is the wavelength shift as a function of temperature (T) and is derived as: ${m\frac{\lambda}{T}} = {{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}{L_{w}.}}}$

[0056] Athermalization of optical waveguide device 20 can then be achieved when ${{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}L_{w}}} = {O.}$

[0057] This assumes that the contributions to thermal change in optical path length due to length changes are negligibly small compared to the contribution due to index of refraction changes, which is found in high silica glass compositions.

[0058] Even though the three coefficients $\frac{N_{3}}{T},\frac{N_{1}}{T},{{and}\quad \frac{N_{2}}{T}}$

[0059] are positive, athermalization can be achieved by having the difference in effective index thermal slope, $\frac{\left( {N_{2} - N_{1}} \right)}{T},$

[0060] negative and properly adjusting the length L_(w) of path segments 42, 44. The temperature coefficient $\frac{\left( {N_{2} - N_{1}} \right)}{T}$

[0061] is related to the widths w₁ and w₂ and to the temperature coefficient $\frac{\left( {N_{core} - N_{clad}} \right)}{T}$

[0062] which is not zero because of the boron concentration difference −B between the core composition (for example B_(core)=1 wt. % B₂O₃) and the cladding composition (for example B_(clad)=8 wt. % B₂O₃).

[0063] The mode effective index, such as N₁, N₂ and N₃, associated to a waveguide of width w, such as w₁, w₂ and w₃, is a combination of the refractive indexes of the core composition and the cladding composition weighted by the fraction of the mode field that is propagated within each of the layers (core/cladding), and is given by the following:

N=[ƒ(w)]N _(core)+[1−ƒ(w)]N _(clad);

[0064] wherein ƒ(w) is the fraction of the mode field propagated within the core composition material and 1−ƒ(w) is the fraction of the mode field propagated within the cladding composition material. Determining N₁, N₂ and N₂−N₁ for waveguide path segment 42 with width w₁ and waveguide path segment 44 with width w₂ is provided by the following equations:

N ₁=[ƒ(w₁)]N _(core)+[1−ƒ(w₁)]N _(clad)

N ₂=[ƒ(w₂)]N _(core)+[1−ƒ(w₂)]N _(clad)

N ₂ −N ₁=[ƒ(w₂)−ƒ(w₁)][N _(core) −N _(clad])

[0065] The temperature (T) dependence of the mode effective index difference N₂−N₁ is then given by the following: $\frac{\left( {N_{2} - N_{1}} \right)}{T} = {\left\lbrack {{f\left( w_{2} \right)} - {f\left( w_{1} \right)}} \right\rbrack {\frac{\left\lbrack {N_{core} - N_{clad}} \right\rbrack}{T}.}}$

[0066] Then using the substitution of: $\frac{\left\lbrack {N_{core} - N_{clad}} \right\rbrack}{T} = {\frac{}{T}\left\lbrack {\frac{N}{B}\Delta \quad B} \right\rbrack}$

[0067] in that the index temperature coefficients of the core and the clad are predominately related to boron concentration and only to a lesser degree effected by variation of GeO₂, P₂O₅, and SiO₂;

[0068] wherein −B is the boron concentration change between the core composition and the cladding composition, the athermalization condition is provided by the following: ${\frac{\left( {N_{2} - N_{1}} \right)}{T} = {\left\lbrack {{f\left( w_{2} \right)} - {f\left( w_{1} \right)}} \right\rbrack \frac{^{2}N}{{TdB}}\Delta \quad B}};\quad {and}$ ${{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{\quad T}L_{w}}} = 0$

[0069] The athermalized optical waveguide device 20 of the invention, includes for example, a Mach-Zehnder interferometer with a path length difference −L=80 μm, which provides a wavelength periodicity of about 20 nm between spectral features. The Mach-Zehnder interferometer silica glass core composition is comprised of 15.6 wt. % GeO₂, 1.1 wt. % B₂O₃, 0.7 wt. % P₂O₅, and 82.6 wt. % SiO₂, and has an index of refraction of approximately 1.455. The Mach-Zehnder interferometer silica glass cladding composition is comprised of 7.9 wt. % B₂O₃, 2.1 wt. % P₂O₅, and 90 wt. % SiO₂, and has an index of refraction of approximately 1.444. These compositions are deposited on a fused silica substrate using flame hydrolysis deposition. Channel waveguides are patterned and formed using photolithography and reactive ion etching. As shown in FIG. 1, input straight waveguide 24 could have a length of about 5000 μm and a path width w₃=6.5 μm, second waveguide core arm 34 having a curvature of radius R=10,000 μm, Y coupler 30 having a length of about 2800 μm, proximity coupler 36 having a length of about 2000 μm and coupler path widths of w₃=6.5 μm, output waveguides 26 and 28 having a length of about 2600 μm and widths of w₃=6.5 μm and separated at their ends by about 350 μm. This Mach-Zehnder interferometer example has a core-clad −=0.75% and the remainder path segments 46 have w₃=6.5 μm. Given a w₁=10 μm for path segment 42 and w₂=3 μm for path segment 44, the fraction of the mode field which is propagated within the waveguide core is respectively ƒ(w₁=10 μm)=0.89 and ƒ(w₂=3 μm)=0.49.

[0070] The temperature coefficient d(N₂−N₁)/dT is calculated as $\frac{\left( {N_{2} - N_{1}} \right)}{T} = {{- 2.1} \times {10^{- 7}/{^\circ}}\quad {C.}}$

[0071] The temperature coefficient d(N₂−N₁)/dT is calculated from d²N/(dTdB) which is a factor that is representative of the core and clad materials and can be determined by analysis of the core and clad materials.

[0072] Using the index temperature coefficient of silica dN/dT=10.5×10⁻⁶ /C^(o) as an approximate value for the remainder path segments 46 as $\frac{N_{3}}{T}$

[0073] in the athermal condition of ${{{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}L_{w}}} = O},$

[0074] provides a means to determine the order of magnitude of L_(w). The actual value of dN/dT will slightly differ from the value for silica because of the other components in the glass composition, but this can be taken into account by minor adjustment of the lengths of path segments 42 and 44. With ΔL=80 μm, and d(N₂−N₁)/dT=−2.1×10⁻⁷/° C., the athermal condition is met with L_(w)=4000 μm. With the length of L_(w) path segments 42, 44 equal to 4000 μm, the path segments 42 and 44 comprise about 20% of the length of optical waveguide device 20.

[0075] Athermalized waveguide device 20 may have more than two waveguide core arms. When athermalized waveguide device 20 comprises a wavelength division multiplexer/demultiplexer, athermalized waveguide device 20 may include a plurality of waveguide core arms. In such a wavelength division multiplexer/demultiplexer the plurality of waveguide core arms are in the form of a phased array, also known as a phasar. In such a multiplexer/demultiplexer the phased array of waveguide core arms may include approximately a hundred waveguide core arms.

[0076]FIG. 4 shows an example of an athermalized waveguide device 20 comprising a multiplexer/demultiplexer 120 which included a phased array 140 of waveguide core arms 32, 34, 103, 104, and 105. For illustrative purposes, FIG. 4 provides an example of such a multiplexer/demultiplexer having only five waveguide core arms, wherein operation such a multiplexer/demultiplexer would include 3 or more waveguide core arms, and usually would include many more waveguide core arms, usually as many as about 100. Multiplexer/demultiplexer 120 as referenced in the direction for demultiplexing, further includes couplers 130 and 136, waveguide input 201, and waveguide outputs 301, 302, 303, and 304. Coupler 130 may couple an optical signal comprised of four wavelength channels from input 201 into waveguide core arms 32, 34, 103, 104, and 105 which function to separate the optical signal into its four wavelength channels which are coupled by coupler 136 into outputs 301, 302, 303, and 304.

[0077] In FIG. 4, waveguide core arm 32 is comprised of a path segment 42 having a waveguide core dimension of w₁, path segments 46 having a waveguide core dimension w₃, and adiabatic tapers 48 between path segments 46 and path segment 42. Waveguide core arm 34 is comprised of a path segment 44 having a waveguide core dimension of w₂, path segments 46 having a waveguide core dimension w₃, and adiabatic tapers 50 between path segments 46 and path segment 44.

[0078] Waveguide core arm 103 is comprised of a path segment 146 having a waveguide core dimension w₁₀₃, path segments 46 having a waveguide core dimension w₃, and adiabatic tapers 152 between path segments 46 and path segment 146. Waveguide core arm 104 is comprised of a path segment 148 having a waveguide core dimension w₁₀₄, path segments 46 having a standard waveguide core dimension w₃, and adiabatic tapers 154 between path segments 46 and path segment 148. Waveguide core arm 105 is comprised of a path segment 150 having a waveguide core dimension w₁₀₅, path segments 46 having a waveguide core dimension w₃, and adiabatic tapers 156 between path segments 46 and path segment 150. First, second, third, fourth, and fifth waveguide core dimensions w₁, w₂, w₁₀₃, w₁₀₄, and w₁₀₅ are unequal.

[0079]FIG. 5 provides another embodiment of an athermalized waveguide device 20 comprising a multiplexer/demultiplexer 120. The phased array 140 of waveguide core arms 32, 34, 103, 104, and 105 include path segments 42 of varying length having a waveguide core arm dimension w₁ and path segments 44 of varying length having a waveguide core arm dimension w₂, in a cascaded fashion with the sum of the lengths of path segment 42 and 44 being the same for the waveguide core arms. The length of path segment 42 in each of the waveguide core arms incrementally varies from the first waveguide core arm to the highest number waveguide core arm. Accordingly the length of path segment 44 increases as the length of path segment 42 decreases. Waveguide core arms 32, 34, 103, 104, and 105 include path segments 46 having a standard waveguide core arms dimension w₃. Waveguide core arms 32, 34, 103, 104, and 105 include adiabatic tapers 50 between path segments 46 and path segments 44; adiabatic tapers 49 between path segments 44 and path segments 42; and adiabatic tapers 48 between path segments 42 and path segments 46.

[0080] Multiplexer/demultiplexers 120 as shown in FIG. 4 and 5 are athermalized using principles of the invention as described in relation to the embodiment shown in FIG. 1. The phased array of waveguide core arms in a multiplexer/demultiplexer can be seen as an interferometer with more than two optical paths in the interferometric section, and may have up to about 100 waveguide core arms in the interferometric section. In the multiplexer/demultiplexer the optical path difference (OPD) between two adjacent paths and the center wavelength (λ) are related by:

OPD=N−L=mλ;

[0081] wherein N is the mode field effective index, −L is the path length increase, and m is an integer.

[0082] In the embodiment of FIG. 5, the length of path segment 44 plus the length of path segment 42 is 1. Path segment 42 has a mode field effective index N₁ associated to the waveguide width dimension of w₁. Path segment 44 has an a mode field effective index N₂ associated to the waveguide width dimension of w₂. Path segments 46 have a mode field effective index N₃ associated to the waveguide width dimension of w₃. The lengths of path segment 42 and 44 are varied depending on the waveguide core arms position in the phased array. When k is the position of the waveguide core arm in the phased array, the length of path segment 42 is given as l_(k) (w₁) and the length of path segment 44 is given as l_(k) (w₂) with the sum of these lengths kept constant by:

l_(k)(w₁)+l_(k)(w₂)=1.

[0083] The optical path length difference (OPD) between two adjacent waveguide paths can be related by:

OPD=N ₃ ΔL+N ₁(l_(k)(w₁)−l_(1−k)(w₁))+N ₂(l_(k)(w₂)−l_(k−1)(w₂)=mλ;

OPD=N ₃ ΔL+(N ₂ −N ₁)(l_(k)(w₂)−l_(k−1)(w₂))=mλ.

[0084] Athermalization (dλ/dT≅0 nm/° C.) may be achieved when the following condition is met: ${{l_{k}\left( w_{2} \right)} - {l_{k - 1}\left( w_{2} \right)}} = {{- \left( {{l_{k}\left( w_{1} \right)} - {l_{k - 1}\left( w_{1} \right)}} \right)} = {\frac{{- {N_{3}}}/{T}}{{\left( {N_{2} - N_{1}} \right)}/{T}}\Delta \quad {L.}}}$

[0085] With w₁=10 μm, w₂=3 μm, dN₃/dT=10.5×10⁻⁶/° C. for the silica index temperature dependence, d(N₂−N₁)/dT=−2.1×10⁻⁷/° C., ΔL=80 μm, the athermalization condition of ${{{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}l}} = O};$

[0086] is met when l=4000 μm,

[0087] with l defined as being l_(k)(w²)−l_(k−1)(w²)=−(l_(k)(w1)−l_(k−1)(w1)) . Such athermalized multiplexer/demultiplexer may be made more compact by utilizing material compositions that provide a greater difference in thermal index shift slope (nm/° C.) between the core composition and the cladding composition.

[0088] It will be apparent to those skilled in the art that various modifications and variations can be made in the structures, designs, compositions, and methods of the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of the invention provided they come within the scope of the appended claims and their equivalents. 

What is claimed is:
 1. An athermalized integrated optical waveguide device comprising: a planar substrate; a first waveguide core arm formed on said planar substrate; a second waveguide core arm formed on said planar substrate; and a waveguide cladding which optically clads said first waveguide core arm and said second waveguide core arm, wherein said first waveguide core arm and said second waveguide core arm have a difference in an effective index thermal slope d(N₁−N₂)/dT.
 2. The athermalized integrated optical waveguide device of claim 1 further comprising: a plurality of waveguide core arms in addition to the first waveguide core arm and the second waveguide core arm.
 3. The athermalized integrated optical waveguide device of claim 1 wherein the first waveguide core arm and the second waveguide core arm each include a core composition, and wherein the waveguide cladding includes a cladding composition.
 4. The athermalized integrated optical waveguide device of claim 3 wherein the core composition and the cladding composition have a difference in thermal spectral index shift slope (nm/° C.).
 5. The athermalized integrated optical waveguide device of claim 3 wherein the core composition is a silica glass.
 6. The athermalized integrated optical waveguide device of claim 5 wherein the core composition includes GeO₂, B₂O₃, P₂O₅, and SiO₂.
 7. The athermalized integrated optical waveguide device of claim 3 wherein the cladding composition is a silica glass.
 8. The athermalized integrated optical waveguide device of claim 7 wherein the cladding composition includes B₂O₃, P₂O₅, and SiO₂.
 9. The athermalized integrated optical waveguide device of claim 3 wherein the core composition or the cladding composition or both include a dopant for controlling thermal spectral index shift slope (nm/° C.) at a concentration, and there is a difference in the concentration of said dopant for controlling thermal spectral index shift slope (nm/° C.) between the core composition and the cladding composition.
 10. The athermalized integrated optical waveguide device of claim 9 wherein the dopant includes boron, and the difference in concentration of the dopant for controlling thermal spectral index shift slope (nm/° C.) is a difference in boron concentration.
 11. The athermalized integrated optical waveguide device of claim 10 wherein the difference in the concentration of the core composition and the cladding composition is between about 3 wt. % B₂O₃ and about 11 wt. % B₂O₃.
 12. The athermalized integrated optical waveguide device of claim 10 wherein the difference in the concentration of the core composition and the cladding composition is between about 5 wt. % B₂O₃ and about 9 wt. % B₂O₃.
 13. The athermalized integrated optical waveguide device of claim 10 wherein the difference in the concentration of the core composition and the cladding composition is between about 6 wt. % B₂O₃ and about 8 wt. % B₂O₃.
 14. The athermalized integrated optical waveguide device of claim 10 wherein the difference in the concentration of the core composition and the cladding composition is approximately 7 wt. % B₂O₃.
 15. The athermalized integrated optical waveguide device of claim 10 wherein the difference in concentration of the dopant for controlling thermal spectral index shift slope (nm/° C.) provides a first d²N/(dTdB) value between the core composition and the cladding composition that is greater than a second d²N/(dTdB) value between the core composition and the cladding composition that has a difference in the concentration of boron.
 16. The athermalized integrated optical waveguide device of claim 1 wherein the first waveguide core arm defines a path segment having a waveguide core dimension of w₁, and the second waveguide core arm defines a path segment having a waveguide core dimension of w₂, wherein w₁ is not equal to w₂.
 17. The athermalized integrated optical waveguide device of claim 16 wherein the first waveguide core arm is a first waveguide core composition, the second waveguide core arm is a second waveguide core composition, and the waveguide cladding is a cladding composition.
 18. The athermalized integrated optical waveguide device of claim 16 wherein the waveguide core dimension w₁ and the waveguide core dimension of w₂ are each a waveguide core width.
 19. The athermalized integrated optical waveguide device of claim 16 wherein the waveguide core dimension w₁ and the waveguide core dimension w₂ are each a waveguide core thickness.
 20. The athermalized integrated optical waveguide device of claim 16 wherein the first path segment of the first waveguide core arm having the waveguide core dimension w₁ is substantially parallel with the fourth path segment of the second waveguide core arm having the waveguide core dimension w₂.
 21. The athermalized integrated optical waveguide device of claim 16 wherein the first waveguide core arm defines a fifth path segment having a waveguide core dimension w₃ and the second waveguide core arm defines a sixth path segment having a waveguide core dimension w₃.
 22. The athermalized integrated optical waveguide device of claim 21 wherein the first waveguide core arm defines an adiabatic taper between the fifth path segment having a waveguide core dimension w₃ and the sixth path segment having a waveguide core dimension w₁.
 23. The athermalized integrated optical waveguide device of claim 16 wherein the length of the first path segment of the first waveguide core arm having the waveguide core dimension w₁ is substantially equal to the length of the fourth path segment of the second waveguide core arm having the waveguide core dimension w₂.
 24. The athermalized integrated optical waveguide device of claim 1 wherein the first waveguide core arm defines a first path segment having a waveguide core dimension w₁ and a second path segment having a waveguide core dimension of w₂, the second waveguide core arm defines a third path segment having a waveguide core dimension w₁ and a fourth path segment having a waveguide core dimension w₂, wherein the length of the first path segment of the first waveguide core arm having a waveguide core dimension w₁ is not equal to the length of the third path segment length of the second waveguide core arm having a waveguide core dimension w₁.
 25. The athermalized integrated optical waveguide device of claim 24 wherein the length of the first path segment of the first waveguide core arm having a waveguide core dimension w₂ is not equal to the length of the fourth path segment of the second waveguide core arm having a waveguide core dimension w₂.
 26. The athermalized integrated optical waveguide device of claim 1 wherein the athermalized integrated optical waveguide device is an interferometer.
 27. The athermalized integrated optical waveguide device of claim 1 wherein the athermalized integrated optical waveguide device is a filter.
 28. The athermalized integrated optical waveguide device of claim 1 wherein the athermalized integrated optical waveguide device is a wavelength division multiplexer or a wavelength division demultiplexer.
 29. The athermalized integrated optical waveguide device of claim 1 wherein the athermalized integrated optical waveguide device is a phased array.
 30. The athermalized integrated optical waveguide device of claim 1 wherein the length of said the waveguide core arm has a first length and the said second waveguide core arm has a second length not equal to said first length.
 31. The athermalized integrated optical waveguide device of claim 1 wherein the athermalized integrated optical waveguide device further comprises: a first coupler; and a second coupler.
 32. A method for making an integrated optical waveguide device comprising the steps performed either sequentially or nonsequentially of: providing a planar substrate; forming a first waveguide core arm of a silica glass core composition on said planar substrate, said first waveguide core arm defining a first path segment having a waveguide core dimension w₁, a second path segment having a waveguide core dimension w₃, and a first optical path length; forming a second waveguide core arm of said silica glass core composition, said second waveguide core arm including a third path segment having a waveguide core dimension w₂, a fourth path segment having a waveguide core dimension w₃, and a second optical path length not equal to said first optical path length of said first waveguide core arm so as to define a difference in optical path lengths ΔL equal to the difference between the optical path length of said first waveguide core arm and the optical path length of said second waveguide core arm; cladding said first waveguide core arm and said second waveguide core arm with a silica glass cladding composition; providing said silica glass core composition with a boron concentration B_(core); and providing said silica glass cladding composition with a boron concentration B_(clad), wherein said boron concentration B_(clad) is different from said boron concentration B_(core) of said core composition
 33. The method of claim 32 wherein the steps of forming the first waveguide core arm and the second waveguide core arm include the step of: depositing a core layer of the silica glass core composition over the planar substrate and exposing said core layer with an image containing a pattern corresponding to the first waveguide core arm and the second waveguide core arm.
 34. The method of claim 32 wherein the first path segment of the first waveguide core arm having a waveguide core dimension w₁ is substantially parallel to the fourth path segment of the second waveguide core arm having a waveguide core dimension w₂.
 35. The method of claim 32 wherein the first path segment of the first waveguide core arm having a waveguide core dimension w₁ has a length L_(w), and the fourth path segment of the second waveguide core arm having a waveguide core dimension w₂ has a substantially equal length L_(w).
 36. The method of claim 35 wherein the method further comprises the step of: optimizing the difference in optical path lengths ΔL, waveguide core dimension w₁, waveguide core dimension w₂, length L_(w), and the difference between the boron concentration B_(core) in the core composition and the boron concentration B_(clad) in the cladding composition to produce an athermal interferometer.
 37. A method for making an integrated optical waveguide device for use in an environment having a temperature which changes, said method comprising the steps performed either sequentially or non-sequentially of: providing a planar substrate; providing a first waveguide arm and a second waveguide arm on said planar substrate, said first waveguide arm and said second waveguide arm each having a length defining a difference in lengths of −L, said first waveguide arm and said second waveguide arm each including a core composition having a high index of refraction and a boron concentration B_(core), said first waveguide arm defining a first segment having a length L_(w) and a waveguide dimension w₁, a remainder of said first waveguide arm having a waveguide dimension w₃, said second waveguide arm defining a second segment having a length L_(w) and a waveguide dimension w₂, the remainder of said second waveguide arm having a waveguide dimension w₃; cladding said first waveguide arm and said second waveguide arm with a cladding composition having a low index of refraction, and a boron concentration B_(clad) different from said boron concentration B_(core) of said core composition so as to define a difference −B between said boron concentration B_(core) of said core composition and said boron composition B_(clad) of said cladding composition; and athermalizing said integrated optical waveguide device by optimizing said difference in lengths −L, said length L_(w), said waveguide dimension w₁, said waveguide dimension w₂, said waveguide dimension w₃, and said difference −B between said boron concentration B_(core) of said core composition and said boron composition B_(clad) of said cladding composition to provide a zero or near-zero thermal spectral shift when said integrated optical waveguide device is subjected to a change in the temperature.
 38. The method of claim 37 wherein the first segment having the length L_(w) and the waveguide dimension w₁ has a mode field effective index N₁ dependent on the waveguide dimension w₁, the second segment having a length L_(w) and a waveguide dimension w₂ has a mode field effective index N₂ dependent on the waveguide dimension w₂, and the remainder of the first waveguide arms and the remainder of the second waveguide arm each having a waveguide dimension w₃ have a mode field effective index N₃, wherein ${{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}L_{w}}} \cong {O.}$


39. An integrated optical waveguide interferometer for use in an environment in which a temperature changes, said integrated optical waveguide interferometer comprising: a first channel waveguide arm having a first length and a second channel waveguide arm having a second length, said first length and said second length defining a difference in length ΔL, said first channel waveguide arms and said second channel waveguide arm having a core composition, said first channel waveguide arm including a first segment of length L_(w), a channel waveguide width w₁ and a mode field effective index N₁ dependent upon said channel waveguide width w₁, said first channel waveguide arm including a second segment having a channel waveguide width w₃, and a mode field effective index N₃ dependent upon said channel waveguide width w₃, said second channel waveguide arm having a third segment of length L_(w), a channel waveguide width w₂ and a mode field effective index N₂ dependent upon said channel waveguide width w₂, said second channel waveguide arm having a fourth segment having a channel waveguide width w₃, and a mode field effective index N₃ dependent upon the channel waveguide width w₃, a waveguide cladding composition, said waveguide cladding composition optically cladding said first channel waveguide arm and said second channel waveguide arm, at least said core composition or said cladding composition or both having a concentration of a dopant for controlling thermal spectral index shift slope (nm/° C.) and defining a difference ΔB between said concentration of said dopant in said core composition and in said cladding composition, said integrated optical waveguide interferometer being substantially insensitive to a change in the temperature when ${{\frac{N_{3}}{T}\Delta \quad L} + {\frac{\left( {N_{2} - N_{1}} \right)}{T}L_{w}}} \cong {O.}$


40. The integrated optical waveguide interferometer of claim 39 wherein the cladding composition and the core composition include silica glass.
 41. The integrated optical waveguide interferometer of claim 39 wherein the dopant for controlling thermal spectral index shift slope (nm/° C.) includes boron.
 42. The athermalized integrated optical waveguide device of claim 41 wherein the difference ΔB in the concentration of the dopant between the core composition and the cladding composition is between about 5 wt. % B₂O₃ and about 9 wt. % B₂O₃.
 43. The athermalized integrated optical waveguide device of claim 41 wherein the difference ΔB in the concentration of the dopant between the core composition and the cladding composition is between about 6 wt. % B₂O₃ and about 8 wt. % B₂O₃.
 44. The athermalized integrated optical waveguide device of claim 41 wherein the difference ΔB in the concentration of the dopant between the core composition and the cladding composition is about 7 wt. % B₂O₃.
 45. The integrated optical waveguide interferometer of claim 39 wherein the concentration of the dopant for controlling thermal spectral index shift slope (nm/° C.) in the either the core composition or the cladding composition or both is not equal to zero.
 46. The integrated optical waveguide interferometer of claim 45 wherein the dopant for controlling thermal spectral index shift slope (nm/° C.) includes boron. 